I always use it quoting Pseudolus: “I’ll be back in a nonce. At most two nonces,”
I know “nonce” in the US sense. I was alerted to the UK sense in Spelling Bee discussions.
Ooh, good one!
I heard the derivation that its short for “nonsense crime” and it came from British prisons and originally meant any crime that didn’t make sense, e.g. random violence, crimes against children, etc. as opposed to regular crimes like burglary, assault, etc. that do “make sense”. But came to mean specifically pedophiles.
No idea if that’s the actual origin, I have no cites.
Wow, as an American I had no idea there were any slang meanings – I know it only as a very, very old-fashioned word for “occasion,” mostly used in the phrase “for the nonce,” or sometimes “nonce word.”
My other association with the word is that medieval and early modern writers tend to use “for the nonce” as generic filler, the same way we might use “you know.” Thus, Chaucer tells us that the Miller “was a stout carl [a strong churl] for the nones,” even though one assumes that he was a big, strong guy on all other occasions as well, and didn’t just bulk up to go on pilgrimage 
The OED does list its “sexual deviant” meaning, and says this about the etymology:
Origin unknown. Perhaps related to nance n., or perhaps compare English regional nonse good-for-nothing fellow, recorded in Eng. Dial. Dict. Suppl. from Lincolnshire.